We study routing for on-demand last-mile logistics with two crucial novel features: i) Multiple depots, optimizing where to pick-up every order, ii) Allowing vehicles to perform depot returns prior to being empty, thus adapting their routes to include new orders online. Both features result in shorter distances and more agile planning. We propose a scalable dynamic method to deliver orders as fast as possible. Following a rolling horizon approach, each time step the following is executed. First, define potential pick-up locations and identify which groups of orders can be transported together, with which vehicle and following which route. Then, decide which of these potential groups of orders will be executed and by which vehicle by solving an integer linear program. We simulate one day of service in Amsterdam that considers 10,000 requests, compare results to several strategies and test different scenarios. Results underpin the advantages of the proposed method

翻译：我们研究了一种面向按需"最后一公里"物流的路径规划问题，具备两个关键创新特性：i) 多仓库模式，可优化每个订单的取货地点；ii) 允许车辆在未清空前返回仓库，从而动态调整路线以纳入新订单。这两个特性均可缩短运输距离并实现更灵活的规划。我们提出一种可扩展的动态方法，旨在以最快速度完成订单配送。该方法采用滚动时域策略，在每个时间步执行以下操作：首先，定义潜在取货点，并识别哪些订单组可被同一车辆沿同一路线协同运输；随后，通过求解整数线性规划，决定执行哪些潜在订单组及由哪辆车执行。我们在阿姆斯特丹模拟了一天的服务场景（包含10,000个请求），将结果与多种策略进行对比，并测试了不同场景下的表现。实验结果表明了所提方法的优势。